Neave, Wesley and Carl had some beads in the ratio of 2 : 3 : 5. Carl gave 40% of his beads to Neave and Wesley. As a result, Neave had the same number of beads as Wesley and Carl had 20 fewer beads than Neave.
- What was the percentage increase in Neave's beads after receiving from Carl?
- How many beads did Wesley have at first?
| Neave |
Wesley |
Carl |
Total |
| 2 u |
3 u |
5 u |
10 u |
| + 2 u |
- 2 u |
|
| 3.5 u |
3.5 u |
3 u |
10 u |
(a)
Number of beads that Carl gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of beads that Neave and Wesley each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of beads that Neave had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Neave's beads after receiving from Carl
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 20
3.5 u - 3 u = 20
0.5 u = 20
1 u = 20 ÷ 0.5 = 40
Number of beads that Wesley had at first
= 3 u
= 3 x 40
= 120
Answer(s): (a) 75%; (b) 120
